I can tell you that is not how mine worked. I was told that my annual fee would be the increased amount on the anniversary of my Bold card when I did the PC to Bountiful. When I did the PC from Bountiful to RC a week later I was told that my annual fee would be the increased amount on the anniversary my current card which they verified to me and it was the same date as the original Bold. Were they wrong?
I have not seen any prorated charge or charge of any type for the new card yet. But if I do, I will post the DP.